Find the Equation Using Point-Slope Formula (-4,-3) , (3,4)

$(- 4, - 3)$ , $(3, 4)$

Step 1

Find the slope of the line between $(- 4, - 3)$ and $(3, 4)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{4 - (- 3)}{3 - (- 4)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 3$ .

$m = \frac{4 + 3}{3 - (- 4)}$

Add $4$ and $3$ .

$m = \frac{7}{3 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{7}{3 + 4}$

Add $3$ and $4$ .

$m = \frac{7}{7}$

Divide $7$ by $7$ .

$m = 1$

Step 2

Use the slope $1$ and a given point $(- 4, - 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 3) = 1 \cdot (x - (- 4))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 3 = 1 \cdot (x + 4)$

Step 4

Solve for $y$ .

Multiply $x + 4$ by $1$ .

$y + 3 = x + 4$

Move all terms not containing $y$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$y = x + 4 - 3$

Subtract $3$ from $4$ .

$y = x + 1$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = x + 1$

Point-slope form:

$y + 3 = 1 \cdot (x + 4)$

Step 6

Find the Equation Using Point-Slope Formula (-4,-3) , (3,4)

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